


The Principle of Marginality and Curing the Common Cold

by Bitenomnom



Series: Mathematical Proof [11]
Category: Sherlock (TV)
Genre: Friendship, Gen, Mathematics, Nightmares, Sherlock with the cold/flu, playing with hair, put on your Johnlock goggles if you'd like
Language: English
Status: Completed
Published: 2012-09-20
Updated: 2012-09-20
Packaged: 2017-11-14 16:03:34
Rating: Not Rated
Warnings: Creator Chose Not To Use Archive Warnings
Chapters: 1
Words: 1,271
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/517109
Author URL: https://archiveofourown.org/users/Bitenomnom/pseuds/Bitenomnom
Summary: <blockquote class="userstuff">
              <p>“I’m sorry,” John sighed. “That was…well. You didn’t exactly get the perfect flatmate either.” They didn’t talk about the shouts in the middle of the night, or of the broken dishes in the trash can the next morning after John came down for a glass of water with a shaky hand.</p>
            </blockquote>





	The Principle of Marginality and Curing the Common Cold

**Author's Note:**

> We mostly did a bunch of computer stuff in class, so this is what I had to work with. XD I hope the math bit comes through, but I'm not sure it does. Ah well. (And, guys, maybe you should be grateful, because if I would've had more time, I was going to try to make this John's side of the story in "Touching." But I didn't have time, so, yeah. Maybe another day. Wish I'd had more time in general -- I wanted to do more with this. But again, it's 4am.) And yes, for the second bit, I was just using the fact that we used the fever drug example in class, not the actual math for that part. Because sometimes the title is just too catchy to not use.
> 
> Speaking of titles, I just realized that even the two fics I've got that aren't from this series both refer to math stuff in the titles. That'll change by the time Saturday's out, though, because my Red Pants contest story does not have a mathematical title.

(1) The Principle of Marginality: If you create a linear model that includes a higher-order term (such as interaction, as mentioned at the beginning of “Touching”), you should also include the individual lower-order “relatives” of that term. For instance, if you have interaction X1D1 in the model, then you should also include X1 and D1 by themselves.

 

(2) Analysis of variance, which involves comparing the amount of data you can explain to the amount you can’t, is just a regression model that only includes dummy variables (also discussed at the beginning of “Touching”). For instance, if you were testing a drug meant to decrease the time it takes to get rid of a fever, you might use a dummy variable to separate subjects that were administered a placebo from those who were administered the drug, and write the time it takes for a patient to cease to have a fever as:

 

T = α + δ1D1 \+ ε

 

with D1 as your dummy variable. It would be 0 for the placebo group, and 1 for the drug group, and you would expect δ1 to be some negative number if the time gets smaller with the drug. (In other words, if the patient is in the placebo group, you just have α and the error term. If they got the drug, some time will be subtracted off.)

 

 

***

 

 

            “John, are you very certain this is necessary?” Sherlock asked, albeit through a stuffed nose and thick phlegm.

            “Very,” John set another glass of water on the table and grabbed the blanket that Sherlock had thrown off the sofa. He wrapped it around Sherlock, who was sprawled out across the sofa and making valiant but unsuccessful attempts at convincing John that he was perfectly fit to carry on with work as usual by doing such foolish things as pestering Lestrade for a new case. John, of course, had given him plenty of warning, and insisted that no matter how persistent Sherlock became, he was not to be running about London at least until after his fever broke.

            Sherlock threw his phone to the ground. “Why doesn’t he answer?”

            “Maybe he’s busy doing his job,” John suggested.

Sherlock huffed and tucked his knees up to his chin in a motion that suggested something along the lines of, _But I do his job so much better than he does!_ or possibly just _It’s not fair!_

            “Why aren’t you sick?”

            John tried not to imagine what kind of a state the flat would be in if the both of them were ill at the same time.

            “I already was. I got rid of it just as you caught it, remember? Come on now, blanket on,” John rewrapped it. “You’ll feel much better.”

            “I’d feel much better if I had something to _do_ , John!” He dug his fingers into his hair. “My mind is _dying_!”

            “Let it _rest_. Would you like to watch a film with me to distract you?”

            Sherlock snorted.

            “Right, yes, of course, not nearly mentally stimulating enough to be distracting.” John took a seat in his chair and went for his third attempt of the day at reading the newspaper, wondering how long it would take Sherlock to do something completely stupid this time. He glanced at Sherlock. “Have you ever considered the idea that our complete lack of mutual interests outside of chasing dangerous criminals around London indicates a questionable ability to select flatmates on your part?”

            “The only thing that _matters_ is chasing criminals around London. Anyway, you’re by far the most reasonable flatmate I’ve ever had. You don’t react _terribly_ ridiculously to my perfectly reasonable—”

            “—thumbs in the fridge? Yeah. Did you ever consider that _you’re_ the problem? You can’t expect interacting with somebody to work out well if _one of you_ is prone to growing six types of mold in _the other of you’s_ jam jars without warning.”

            Sherlock seemed taken aback. “I…” _I_ did _tell you about that,_ he was going to say, but then realized that that was probably one of those John-inconveniently-not-at-the-flat-but-rather-at-work-or-on-a-date times.

            “I’m sorry,” John sighed. “That was…well. You didn’t exactly get the perfect flatmate either.” They didn’t talk about the shouts in the middle of the night, or of the broken dishes in the trash can the next morning after John came down for a glass of water with a shaky hand. They especially didn’t talk about the one embarrassing night John had come downstairs to cool his head and flopped down onto the sofa in a daze. He had landed on Sherlock. It had taken him an embarrassingly long time to move—well—he was fairly certain he eventually moved. For a while, he had stayed there, and Sherlock had reached up slowly, as if to a feral dog, to pet John’s hair. John could only remember how it felt when he was half-conscious; he let the memory play in his mind as he tried to sleep, and found it usually helped keep things peaceful—a little, at least. There was still shouting and shattered glass. It would probably never go away.

            “About the experiments…”  
  
            “It’s fine. Forget I said anything. I’m just tired.”

            “I suppose we could both use some rest.”

            “You especially. You’ll recover more quickly that way. Probably why I got better so quickly—you know, because I sleep like a regular human being, rather than, oh, about two hours every other week.”

            “I sleep more than that,” was all Sherlock said, followed by, “Well, why don’t you go back to bed, then? At least one of us could get some rest that way.”

            “Because, Sherlock, I know that the second I go upstairs—or even fall asleep in this chair, as a matter of fact—you’re going to leave the flat and jump into the Thames or something because you thought you saw an interestingly-patterned handkerchief that could only belong to a serial killer.”

            “That’s ridiculous.”

            John raised his eyebrows and stared.

            “Fine. There _is_ away for you to both get some rest and ensure I don’t leave without you knowing. I may fall asleep as well.”

            “Oh?”

            Sherlock patted the area beside him. “You can’t catch it anymore, can you?”

            “Very unlikely,” John agreed, and stood, stepping tentatively toward the sofa. “You want me to…?”

            “If I need to displace you in order to move, it will wake you, and you can prevent me from leaving.” John doubted that, actually—Sherlock was stronger than he looked, and wasn’t prone to a bad shoulder impeding his range of movement, so even with Sherlock’s congestion and nausea it would be a more even fight than John would like to admit—but he nodded. “Additionally, I find it relaxing to…” he trailed off, as if concerned that he might break the spell if he spoke of it. And, John thought, he might. So he simply nodded and then sat on the sofa beside Sherlock. “Go on,” Sherlock said.

            John leaned against him.

            “I’m not sure that will keep me in place.”

            John pulled back to stare at Sherlock.

            “I won’t mention it to anybody. Not Mrs. Hudson, not your girlfriends. Not even you, if you wish. Is that agreeable?”

            John nodded, and couldn’t hold back a smile. Hearing Sherlock, miserable with sickness, attempt to negotiate his way into petting John’s hair since he under John’s care he couldn’t do anything much more exciting than that was admittedly enough to lift John’s mood. He laid his head in Sherlock’s lap, and they both drifted off to the calm, repetitive motion of Sherlock’s fingers through John’s hair.


End file.
